Flow boiling of liquid nitrogen in micro-tubes: Part I – The onset of nucleate boiling, two-phase flow instability and two-phase flow pressure drop

This paper is the first portion of a two-part study concerning the flow boiling of liquid nitrogen in the micro-tubes with the diameters of 0.531, 0.834, 1.042 and 1.931 mm. The contents mainly include the onset of nucleate boiling (ONB), two-phase flow instability and two-phase flow pressure drop. At ONB, mass flux drops suddenly while pressure drop increases, and apparent wall temperature hysteresis in the range of 1.0–5.0 K occurs. Modified Thom model can predict the wall superheat and heat flux at ONB. Moreover, stable long-period (50–60 s) and large-amplitude oscillations of mass flux, pressure drop and wall temperatures are observed at ONB for the 1.042 and 1.931 mm micro-tubes. Block phenomenon at ONB is also observed in the cases of high mass flux. The regions for the oscillations, block and stable flow boiling are classified. A physical model of vapor patch coalesced at the outlet is proposed to explain the ONB oscillations and block. Vapor generation caused by the flash evaporation is so large that it should be taken into account to precisely depict the variation of mass quality along the micro-tube. The adiabatic and diabatic two-phase flow pressure drop characteristics in micro-tubes are investigated and compared with four models including homogeneous model and three classical separated flow models. Contrary to the conventional channels, homogeneous model yields better prediction than three separated flow models. It can be explained by the fact that the density ratio of liquid to vapor for nitrogen is comparatively small, and the liquid and vapor phases may mix well in micro-tube at high mass flux due to small viscosity of liquid nitrogen, which leads to a more homogeneous flow. Part II of this study will focus on the heat transfer characteristics and critical heat flux (CHF) of flow boiling of liquid nitrogen in micro-tubes.     

An experimental study of convective heat transfer in silicon microchannels with different surface conditions

An experimental investigation has been performed on the laminar convective heat transfer and pressure drop of water in 13 different trapezoidal silicon microchannels. It is found that the values of Nusselt number and apparent friction constant depend greatly on different geometric parameters. The laminar Nusselt number and apparent friction constant increase with the increase of surface roughness and surface hydrophilic property. These increases become more obvious at larger Reynolds numbers. The experimental results also show that the Nusselt number increases almost linearly with the Reynolds number at low Reynolds numbers (Re<100), but increases slowly at a Reynolds number greater than 100. Based on 168 experimental data points, dimensionless correlations for the Nusselt number and the apparent friction constant are obtained for the flow of water in trapezoidal microchannels having different geometric parameters, surface roughnesses and surface hydrophilic properties. Finally, an evaluation of heat flux per pumping power and per temperature difference is given for the microchannels used in this experiment.     

Flow boiling of liquid nitrogen in micro-tubes: Part II – Heat transfer characteristics and critical heat flux

This paper is the second portion of a two-part study concerning the flow boiling of liquid nitrogen in the micro-tubes with the diameters of 0.531, 0.834, 1.042 and 1.931 mm. The contents include the heat transfer characteristics and critical heat flux (CHF). The local wall temperatures are measured, from which the local heat transfer coefficients are determined. The influences of heat flux, mass flux, pressure and tube diameter on the flow boiling heat transfer coefficients are investigated systematically. Two regions with different heat transfer mechanism can be classified: the nucleate boiling dominated region for low mass quality and the convection evaporation dominated region for high mass quality. For none of the existed correlations can predict the experimental data, a new correlation expressed by Co, Bo, We, K_p and X is proposed. The new correlation yields good fitting for 455 experimental data of 0.531, 0.834 and 1.042 mm micro-tubes with a mean absolute error (MAE) of 13.7%. For 1.931 mm tube, the flow boiling heat transfer characteristics are similar to those of macro-channels, and the heat transfer coefficient can be estimated by Chen correlation. Critical heat flux (CHF) is also measured for the four tubes. Both the CHF and the critical mass quality (CMQ) are higher than those for conventional channels. According to the relationship that CMQ decreases with the mass flux, the mechanism of CHF in micro-tubes is postulated to be the dryout or tear of the thin liquid film near the inner wall. It is found that CHF increases gradually with the decrease of tube diameter.     

Experimental study for the enhancement of heat transfer characteristics and development of thermal correlations of a roughened solar collector

The thermal performance of the flat plate solar collector is very low. The most beneficial and worthwhile method for increasing the thermal performance of a solar-powered air heater (SPAH) is to include a roughness element in the working zone of heat transfer that is located beneath the shear layer of the absorber surface. In this research work, efforts are made to enhance thermal performance and develop thermal correlations for the estimation of the Nusselt number and friction factor of a roughened SPAH. Experiments are performed for various ranges of flow, Reynolds numbers, and roughness parameters. The experimental technique of liquid crystal thermography is utilized to assess the dispersal of Nusselt number over the roughened surface for all roughness parameters. A maximum thermal performance enhancement index of 2.69 is obtained with the optimum value of the roughness parameter at a relative roughness pitch (RRP) of 9, a relative staggering distance (RSD) of 4, and a relative roughness length (RRL) of 6.15. Second, a mathematical correlation is developed using a regression model to estimate the Nusselt number and friction factor in terms of nondimensional roughness and flow parameters operated as RRP, RSD, RRL, and Re. The degree of discrepancy between the established the relationships and the findings from the experiment reveals incredibly satisfying results. Hence employing twisted V-ribs as an artificial roughness element no doubt increases the Nusselt number, and thermohydraulic performance enhancement index, but it also exerts less frictional power across the SPAH duct.     

Fluid flow and heat transfer of liquid-liquid two phase flow in microchannels: A review

The fluid flow and heat transfer behavior of liquid–liquid two phase flows have led to significantly improve the heat transfer rates in microchannels. Both numerical and experimental studies are reviewed in this paper to gain useful insights into the effect of a number of parameters such as film thickness, Peclet number, working fluid and flow geometry on hydrodynamic and thermal behavior of microchannels using liquid-liquid two phase flow. In addition, the paper summarises information about common correlations proposed to predict the pressure drop and heat transfer coefficient in the form of Nusselt number (Nu). The present study shows that there is little agreement across the literature between measured pressure drop and Nusselt number and predictions based on these correlations. Finally, the conclusions and important summaries, and some possible future development of this field are presented.     

A Review of Heat Transfer and Pressure Drop Correlations for Laminar Flow in Curved Circular Ducts

Heat transfer and pressure drop correlations for fully developed laminar Newtonian fluid flow in curved and coiled circular tubes are reviewed. Curved geometry is one of the passive heat transfer enhancement methods that fits several heat transfer applications, such as power production, chemical and food industries, electronics, environment engineering, and so on. Centrifugal force generates a pair or two pairs of cross-sectional secondary flow (based on the Dean number), which are known as the Dean vortices, and improves the overall heat transfer performance with an amplified peripheral Nusselt number variation. The main purpose of this review paper is to provide researchers with a comprehensive list of correlations and concepts that they may need during their research. The paper begins with an introduction to the governing equations and important dimensionless numbers for the flow in curved tubes. The correlations for developing flow in curved and coiled circular tubes are also presented. The main contribution of this study is reviewing the numerical and experimental correlations to calculate friction factor and Nusselt number in curved circular tubes. Nusselt number correlations are categorized based on the thermal boundary condition, as well as on the method. A Dean number range of 1 to 20,000 for the pressure drop correlations and 1 to 7000 for the heat transfer correlations and a Prandtl number range of 0.1 to 7,000 are covered with the reviewed correlations.     

Thermally developing flow and heat transfer in rectangular microchannels of different aspect ratios

Laminar convective heat transfer in the entrance region of microchannels of rectangular cross-section is investigated under circumferentially uniform wall temperature and axially uniform wall heat flux thermal boundary conditions. Three-dimensional numerical simulations were performed for laminar thermally developing flow in microchannels of different aspect ratios. Based on the temperature and heat flux distributions obtained, both the local and average Nusselt numbers are presented graphically as a function of the dimensionless axial distance and channel aspect ratio. Generalized correlations, useful for the design and optimization of microchannel heat sinks and other microfluidic devices, are proposed for predicting Nusselt numbers. The proposed correlations are compared with other conventional correlations and with available experimental data, and show very good agreement.     

Experimental investigation of turbulent flow and convective heat transfer characteristics of alumina water nanofluids in fully developed flow regime

In this paper the convective heat transfer and friction factor of the nanofluids in a circular tube with constant wall temperature under turbulent flow conditions were investigated experimentally. Al₂O₃ nanoparticles with diameters of 40 nm dispersed in distilled water with volume concentrations of 0.1–2 vol.% were used as the test fluid. All physical properties of the Al₂O₃–water nanofluids needed to calculate the pressure drop and the convective heat transfer coefficient were measured. The results show that the heat transfer coefficient of nanofluid is higher than that of the base fluid and increased with increasing the particle concentrations. Moreover, the Reynolds number has a little effect on heat transfer enhancement. The experimental data were compared with traditional convective heat transfer and viscous pressure drop correlations for fully developed turbulent flow. It was found that if the measured thermal conductivities and viscosities of the nanofluids were used in calculating the Reynolds, Prandtl, and Nusselt numbers, the existing correlations perfectly predict the convective heat transfer and viscous pressure drop in tubes.     

Thermophysical properties,heat transfer and pressure drop of COOH-functionalized multi walled carbon nanotubes/water nanofluids

This paper is a continuation of the authors' previous work on the thermophysical properties, heat transfer, and pressure drop of nanofluids [Experimental Thermal and Fluid Science 52 (2014) 68–78]. In this paper, an experimental study is carried out to study the turbulent flow of COOH-functionalized multi-walled carbon nanotubes/water nanofluid flowing through a double tube heat exchanger. For this purpose, first, the thermophysical properties of the nanofluid, including the thermal conductivity and dynamic viscosity, have been measured at various temperatures and concentrations. Using the measured data, new correlations as a function of temperature and concentration are presented to predict the thermophysical properties. In the next step, the effects of low volume fractions of the nanofluid (from 0.05% to 1%) on the heat transfer rate are studied at the Reynolds numbers between 5000 and 27,000. The experimental results reveal that with increasing the nanofluid concentration, the heat transfer coefficient and thermal performance factor increase. On average, a 78% increase in heat transfer coefficient, a 36.5% increase in the average Nusselt number, and a 27.3% penalty in the pressure drop are recorded for the highest concentration of MWCNTs in water.     

Laminar Forced Flow and Heat Transfer in Cross-Corrugated Triangular Ducts

The fluid flow and heat transfer characteristics in a cross-corrugated triangular channel are studied under laminar forced flow and uniform wall temperature conditions. Both the local and the periodic mean values of friction factor and wall Nusselt numbers in the hydro and thermally developing entrance region are investigated. It is found that at higher Reynolds numbers, recirculations in the lower wall valleys are a dominant factor for flow and heat transfer, while at lower Reynolds numbers, parallel flows in the upper wall corrugation are the predominant factor. Compared with a parallel flat plates duct, the Nusselt numbers in a cross-corrugated triangular duct can be enhanced, and can be even higher at higher Reynolds numbers. The growth of steady recirculations and the concomitant periodic disruption and thinning of the boundary layer promote enhanced transport of heat as well as momentum. Effects of heat transfer enhancement are more obvious under higher Reynolds numbers. Two correlations are proposed to predict the periodic mean values of Nusselt numbers and friction factors for Reynolds numbers from 10 to 2000.     

Experimental study of mixed convection and pressure drop in helically dimpled tubes for laminar and transition flow

This paper presents the experimental results carried out in dimpled tubes for laminar and transition flows and completes a previous work of the authors focused on the turbulent region. It was observed that laminar flow heat transfer through horizontal dimpled tubes is produced in mixed convection, where Nusselt number depends on both the natural convection and the entry region. Employing water and ethylene glycol as test fluids, the following flow range was covered: x^*=10⁻⁴–10⁻² and Ra=10⁶–10⁸.

The experimental results of isothermal pressure drop for laminar flow showed dimpled tube friction factors between 10% and 30% higher than the smooth tube ones. Moreover, it was perceived that roughness accelerates transition to critical Reynolds numbers down to 1400. Correlations for the laminar friction factor f=f(Re,h/d) and for the critical Reynolds Re_crit=Re_crit(h/d) are proposed. The hydraulic behaviour of dimpled tubes was found to depend mainly on dimple height.

In mixed convection, high temperature differences in the cross section were measured and therefore heat transfer was evaluated by a circumferentially averaged Nusselt number. Experimenal correlations for the local and the fully developed Nusselt numbers and are given. Results showed that at low Rayleigh numbers, heat transfer is similar to the smooth tube one whereas at high Rayleigh, enhancement produced by dimpled tubes can be up to 30%.     

Single-Phase Cryogenic Flow and Heat Transfer Through Microscale Pin Fin Heat Sinks

Single-phase heat transfer and pressure drop of liquid nitrogen in microscale heat sinks are studied experimentally in this paper. Effects of geometrical variations are characterized on the thermofluidic performance of staggered microscale pin fin heat sinks. Pitch-to-diameter ratio and aspect ratio of the micro pin fins are varied. The pin fins have square shape with 200 or 400 μm width and are oriented at 45 degrees to the flow direction. Thermal performance of the heat sinks is evaluated for Reynolds numbers (based on pin fin hydraulic diameter) from 108 to 570. Results are presented in a nondimensional form in terms of friction factor, Nusselt number, and Reynolds number and are compared with the predictions of existing correlations in the literature for micro pin fin heat sinks. Comparison of flow and heat transfer performance of the micro pin fin heat sinks reveals that at a particular critical Reynolds number of ～250, pin fin heat sinks with the same aspect ratio but larger pitch ratio show a transition in both friction factor and Nusselt number. In order to better characterize this transition, visualization experiments were performed with the Fluorinert PF5060 using an infrared camera. At the critical Reynolds number, for the larger pitch ratio pin fin heat sink, surface thermal intensity profiles suggest periodic flapping of the flow behind the pin fins at a Strouhal number of 0.227.     

Development of correlations for Nusselt number and friction factor for solar air heater with roughened duct having arc-shaped wire as artificial roughness

An experimental study has been carried out for enhancement of heat transfer coefficient of a solar air heater having roughened air duct provided with artificial roughness in the form of arc-shape parallel wire as roughness element. Increment in friction factor by provided with such artificial roughness elements has also been studied. The effect of system parameters such as relative roughness height (e/d) and arc angle (α/90) have been studied on Nusselt number (Nu) and friction factor (f) with Reynolds number (Re) varied from 2000 to 17000. Considerable enhancement in heat transfer coefficient has been achieved with such roughness element. Using experimental data correlations for Nusselt number and friction factor have also been developed for such solar air heaters, which gives a good agreement between predicted values and experimental values of Nusselt number and friction factor.     

Experimental and numerical studies of liquid flow and heat transfer in microtubes

Experimental and numerical studies were conducted to reveal the flow and heat transfer characteristics of liquid laminar flow in microtubes. Both the smooth fused silica and rough stainless steel microtubes were used with the hydraulic diameters of 50–100 μm and 373–1570 μm, respectively. For the stainless steel tubes, the corresponding surface relative roughness was 2.4%, 1.4%, 0.95%. The experiment was conducted with deionized water at the Reynolds number from 20 to 2400. The experimental data revealed that the friction factor was well predicted with conventional theory for the smooth fused silica tubes. For the rough stainless steel tubes, the friction factor was higher than the prediction of the conventional theory, and increased as the surface relative roughness increased. The results also confirmed that the conventional friction prediction was valid for water flow through microtube with a relative surface roughness less than about 1.5%. The experimental results of local Nusselt number distribution along the axial direction of the stainless steel tubes do not accord with the conventional results when Reynolds number is low and the relative thickness of the tube wall is high. The numerical study reveals that the large ratio of wall thickness over tube diameter in low Reynolds number region causes significant axial heat conduction in the tube wall, leading to a non-linear distribution of the fluid temperature along the axial direction. The axial heat conduction effect is gradually weakened with the increase of Reynolds number and the decrease of the relative tube wall thickness and thus the local Nusselt number approaches the conventional theory prediction.     

Nusselt number and friction factor correlations for solar air heater duct having artificially roughened absorber plate

An experimental investigation has been carried out for a range of system and operating parameters in order to analyse effect of artificial roughness on heat transfer and friction in solar air heater duct having protrusions as roughness geometry. An increase in heat transfer and friction loss has been observed for duct having roughened absorber plate. Experimental data have been used to develop Nusselt number and friction factor correlations as function of system and operating parameters for predicting performance of the system having investigated type of roughness geometry.     

Hydrodynamics and heat transfer in two-dimensional minichannels

This work presents measurements of the friction and heat transfer coefficients in 2D minichannels of 1.12 mm to 300 μm in thickness. The friction factor is estimated from the measured pressure drop along the whole channel. The heat transfer coefficient is determined from a local and direct measurement of both temperature and heat flux at the wall using a specific transducer. The experimental results are in good agreement with classical correlations relative to channels of conventional size. The observed deviations are explained either by macroscopic effects (mainly entry and viscous dissipation effects) or by imperfections of the experimental apparatus.     

Thermal performance of finned aluminum heat sink filled with ERG aluminum foam: Experimental and numerical approach

The rapid improvements in electronic devices have led to a high demand for effective cooling techniques. The purpose of this study was to investigate the heat transfer characteristics and performance of different aluminum heat sinks filled with aluminum foam for an Intel core i7 processor. The aluminum foam heat sinks were subjected to water flow covering the non-Darcy flow regime (300-600 Reynolds numbers). The bottom side of the heat sinks was heated with a heat flux between 8.5 and 13.8 W/cm². Three different heat sinks were examined in this study. Models A, B, and C contained two, three and four channels, respectively. Each channel gap was filled with ERG aluminum foam. The distributions of the local surface temperature and the local Nusselt number were measured for each heat sink design. The experimental data were compared with the numerical results. The average Nusselt number was obtained for the range of Reynolds numbers, and an empirical correlation of the average Nusselt number as a function of the Reynolds number was derived for each heat sink. The pressure drop across the characteristics of each heat sink design was measured. The thermal performance of each aluminum foam heat sink was evaluated based on the average Nusselt number and the required pumping power. The experimental results revealed that model B achieved the highest average Nusselt number compared with models A and C. However, model C had the highest surface to volume ratio; the thermal boundary layers, which are formed on adjacent fin surfaces inside the aluminum foam, interface with each other causing a reduction in the overall heat transfer. The numerical results were in good agreement with experimental data of local Nusselt number and local temperature with maximum relative errors of 2% and 1%, respectively.     

Thermal characteristics of electroosmotic flow in a wavy-wall microtube

This study numerically investigates the electroosmotic flow and heat transfer in a wavy surface of the micro-tubes. The solution takes the electrokinetic effect and the amplitude of the wavy surface into consideration. A simple coordinate transformation method is used to transform a complex wavy micro-tube into a regular, circular tube. The governing equations, including the Poisson-Boltzmann equation, the modified Navier-Stokes equations, and the energy equation with their corresponding boundary conditions are also transformed into the computational domain and then solved by the finite difference method. The main objective is to investigate the difference of fluid flow and temperature fields for various wavelength ratio a and the electrokinetic parameter β. Results show that the distributions of the skin-friction coefficient and the local Nusselt number are oscillatory along the stream-wise direction for the wavy micro-tube (a ≠ 0). The amplitude of the oscillated local Nusselt number increases with an increase in the electrokinetic parameter β and wavelength ratio a, but that of the skin-friction coefficient decreases with an increase in the electrokinetic parameter β. The heat transfer enhancement is significant for the larger electrokinetic parameter β and wavelength ratio a.     

Investigation of thermal performance of solar air heater having roughness elements as a combination of inclined and transverse ribs on the absorber plate

An experimental investigation has been carried out to study the heat transfer and friction characteristics by using a combination of inclined as well as transverse ribs on the absorber plate of a solar air heater. The experimental investigation encompassed the Reynolds number (Re) ranges from 2000 to 14 000, relative roughness pitch (p/e) 3–8 and relative roughness height (e/D_h) 0.030. The effect of these parameters on the heat transfer coefficient and friction factor has been discussed in the present paper and correlations for Nusselt number and friction factor has been developed within the reasonable limits. A procedure to compute the thermal efficiency based on heat transfer processes in the system is also given and the effect of these parameters on thermal efficiency has been discussed.     

Correlations for solar air heater duct with V-shaped perforated baffles as roughness elements on absorber plate

An experimental investigation has been carried out to study the effect of heat transfer and friction characteristics of air passing through a rectangular duct which is roughened by V-down perforated baffles. The experiment encompassed Reynolds number (Re) from 3800 to 19,000, relative roughness height (e/H) values of 0.285–0.6, relative roughness pitch (P/e) range of 1–4 and open area ratio values from 12% to 44%. The effect of roughness parameters on Nusselt number (Nu) and friction factor (f) has been determined and increase in heat transfer and friction loss has been observed for ducts having a roughened test plate. Maximum Nusselt number is observed for the relative roughness pitch ranging from 1.5 to 3 for flow and geometrical parameters under consideration. The experimental data have been used to develop Nusselt number and friction factor correlations as a function of roughness and flow parameters.